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Completion Without Failure
, 1989
"... We present an "unfailing" extension of the standard KnuthBendix completion procedure that is guaranteed to produce a desired canonical system, provided certain conditions are met. Weprove that this unfailing completion method is refutationally complete for theorem proving in equational theories. The ..."
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Cited by 122 (19 self)
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We present an "unfailing" extension of the standard KnuthBendix completion procedure that is guaranteed to produce a desired canonical system, provided certain conditions are met. Weprove that this unfailing completion method is refutationally complete for theorem proving in equational theories. The method can also be applied to Horn clauses with equality, in which case it corresponds to positive unit resolution plus oriented paramodulation, with unrestricted simplification.
Otter: The CADE13 Competition Incarnations
 JOURNAL OF AUTOMATED REASONING
, 1997
"... This article discusses the two incarnations of Otter entered in the CADE13 Automated Theorem Proving Competition. Also presented are some historical background, a summary of applications that have led to new results in mathematics and logic, and a general discussion of Otter. ..."
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Cited by 44 (3 self)
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This article discusses the two incarnations of Otter entered in the CADE13 Automated Theorem Proving Competition. Also presented are some historical background, a summary of applications that have led to new results in mathematics and logic, and a general discussion of Otter.
The Applications of Theorem Proving to QuestionAnswering Systems
, 1969
"... This paper shows how a questionanswering system can use firstorder logic as its language and an automatic theorem prover, based upon the resolution inference principle, as its deductive mechanism. The resolution proof procedure is extended to a constructive proof procedure. An answer construction ..."
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Cited by 27 (0 self)
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This paper shows how a questionanswering system can use firstorder logic as its language and an automatic theorem prover, based upon the resolution inference principle, as its deductive mechanism. The resolution proof procedure is extended to a constructive proof procedure. An answer construction algorithm is given whereby the system is able not only to produce yes or no answers but also to find or construct an object satisfying a specified condition. A working computer program, QA3, based on these ideas, is described. The performance of the program, illustrated by extended examples, compares favorably with several other questionanswering programs. Methods are presented for solving state transformation problems. In addition to questionanswering, the program can do automatic programming
33 Basic Test Problems: A Practical Evaluation of Some Paramodulation Strategies
, 1996
"... Introduction Many researchers who study the theoretical aspects of inference systems believe that if inference rule A is complete and more restrictive than inference rule B, then the use of A will lead more quickly to proofs than will the use of B. The literature contains statements of the sort "ou ..."
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Cited by 24 (5 self)
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Introduction Many researchers who study the theoretical aspects of inference systems believe that if inference rule A is complete and more restrictive than inference rule B, then the use of A will lead more quickly to proofs than will the use of B. The literature contains statements of the sort "our rule is complete and it heavily prunes the search space; therefore it is efficient". 2 These positions are highly questionable and indicate that the authors have little or no experience with the practical use of automated inference systems. Restrictive rules (1) can block short, easytofind proofs, (2) can block proofs involving simple clauses, the type of clause on which many practical searches focus, (3) can require weakening of redundancy control such as subsumption and demodulation, and (4) can require the use of complex checks in deciding whether such rules should be applied. The only way to determ
The representation of medical reasoning models in resolutionbased theorem provers
 Artificial Intelligence in Medicine
, 1993
"... Firstorder predicate logic essentially is a language to express knowledge concerning objects and relationships between objects in a domain. Many medical problems can be cast naturally in such terms. In this paper the suitability of logic as a knowledgerepresentation formalism in building medical e ..."
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Cited by 14 (5 self)
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Firstorder predicate logic essentially is a language to express knowledge concerning objects and relationships between objects in a domain. Many medical problems can be cast naturally in such terms. In this paper the suitability of logic as a knowledgerepresentation formalism in building medical expert system is investigated. In particular, we investigate the logical representation of three typical reasoning models in medicine: diagnostic, anatomical and causal reasoning. It turns out that each of these models has its own characteristic logical structure. Furthermore, the pragmatics of using theoremproving techniques in consulting such logicbased medical expert systems is discussed. In particular, attention is paid to the use of a metalevel architecture to improve the applicability of theoremproving techniques in building expert systems.
Automated Reasoning and Bledsoe's Dream for the Field
"... In one sense, this article is a personal tribute to Woody Bledsoe. As such, the style will in general be that of private correspondence. However, since this article is also a compendium of experiments with an automated reasoning program, researchers interested in automated reasoning, mathematics, an ..."
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Cited by 7 (6 self)
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In one sense, this article is a personal tribute to Woody Bledsoe. As such, the style will in general be that of private correspondence. However, since this article is also a compendium of experiments with an automated reasoning program, researchers interested in automated reasoning, mathematics, and logic will find pertinent material here. The results of those experiments strongly suggest that research frequently benefits greatly from the use of an automated reasoning program. As evidence, I select from those results some proofs that are better than one can find in the literature, and focus on some theorems that, until now, had never been proved with an automated reasoning program, theorems that Hilbert, Church, and various logicians thought significant. To add spice to the article, I present challenges for reasoning programs, including questions that are still open. 1 This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Depa...
Investigations in Model Elimination Based Theorem Proving
, 1992
"... Automated reasoning systems, also called automatic theorem provers, have been a focus of study since computer science expanded to include the study of symbolic computation in the 1950's. More recently, the socalled "logic programming" language Prolog has been the focus of much study that has genera ..."
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Cited by 6 (3 self)
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Automated reasoning systems, also called automatic theorem provers, have been a focus of study since computer science expanded to include the study of symbolic computation in the 1950's. More recently, the socalled "logic programming" language Prolog has been the focus of much study that has generated very efficient implementations of a language once noted for its expressive power, but now noted for its performance as well. The joining of Prolog technology with an early system of inference called Model Elimination led to the development of theorem proving systems with a very high rate of inference. This dissertation focuses on the study of automated reasoning based on Model Elimination. A theorem proving architecture and system called METEOR is described and is implemented that is the foundation of a reasoning system that runs on sequential computers, NUMA sharedmemory MIMD computers, and in a messagepassing distributed computing environment; this reasoning system has the highest r...